First of all, they had no control group. Secondly, their sample size was very small. thirdly, they make this conclusion:

"This finding may be explained by hypothesizing that older people, although not previously exposed to H5N1 subtype, may have gained protective immunity by previous infections sustained by circulating influenza virus strains,” they wrote.

So the more strains of influenza you're exposed to, the better your immune system reacts. NATURAL strains through natural exposure. Not through a vaccine.